The two rails, separated by 1m, of a railway track are connected to a voltmeter. What will be the reading of the voltmeter when a train travels on the rails with speed 5m/s. The earth's magnetic field at the place is `4xx10^(-4)T`, and the angle of dip is `30^(º)`.

Answer

To solve the problem, we need to calculate the electromotive force (EMF) induced in the rails as the train moves through the Earth's magnetic field. The formula for the induced EMF (E) is given by:

\[ E = B \cdot V \cdot L \cdot \sin(\phi) \]

Where:
- \( E \) is the induced EMF,
- \( B \) is the magnetic field strength,
- \( V \) is the velocity of the train,
- \( L \) is the length of the rails,
- \( \phi \) is the angle between the direction of motion and the magnetic field.

### Step-by-Step Solution:

1. **Identify the given values:**
- Magnetic field strength, \( B = 4 \times 10^{-4} \, T \)
- Velocity of the train, \( V = 5 \, m/s \)
- Length of the rails, \( L = 1 \, m \)
- Angle of dip, \( \phi = 30^\circ \)

2. **Calculate \( \sin(\phi) \):**
- Since \( \phi = 30^\circ \), we know that:
\[ \sin(30^\circ) = \frac{1}{2} \]

3. **Substitute the values into the EMF formula:**
\[ E = B \cdot V \cdot L \cdot \sin(\phi) \]
\[ E = (4 \times 10^{-4} \, T) \cdot (5 \, m/s) \cdot (1 \, m) \cdot \left(\frac{1}{2}\right) \]

4. **Perform the multiplication:**
\[ E = 4 \times 10^{-4} \cdot 5 \cdot 1 \cdot \frac{1}{2} \]
\[ E = 4 \times 5 \times \frac{1}{2} \times 10^{-4} \]
\[ E = 20 \times \frac{1}{2} \times 10^{-4} \]
\[ E = 10 \times 10^{-4} \, V \]

5. **Convert to standard form:**
\[ E = 10^{-3} \, V \]

6. **Convert to millivolts:**
\[ E = 1 \, mV \]

### Final Answer:
The reading of the voltmeter will be \( 1 \, mV \).